quennmochi quennmochi

01-09-2018
Mathematics

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A n-faced regular polyhedron consists of 2n edges and (2n-4) vertices. Find n .

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WojtekR WojtekR

01-09-2018

We could use Euler's polyhedron formula:

[tex] F=n\qquad\qquad\text{(Faces)}\\\\E=2n\qquad\qquad\text{(Edges)}\\\\V=2n-4\qquad\qquad\text{(Vertices)}\\\\\\V-E+F=2\\\\2n-4-2n+n=2\\\\-4+n=2\qquad|+4\\\\\boxed{n=6} [/tex]

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